Boundary Terms of Noether Currents for Gravity from Multisymplectic Geometry

Recent developments in multisymplectic geometry have clarified the connection between conserved Noether currents and symmetry transformations in field theories. In particular, the diffeomorphism invariance of the Einstein-Hilbert action has an associated collection of Noether currents, given by the Einstein tensor. We consider a space+time decomposition of the theory with the spatial slice having non-trivial boundary conditions. Using the multisymplectic formalism to simplify the transition to the space+time framework, we show how easy it is to obtain the ``boundary terms'' for the Noether currents. This is the first known incorporation of surfaces with non-trivial boundary conditions into this particular type of multisymplectic formalism. For asymptotically flat spacetimes, these boundary terms, in turn, have a clear, transparent, connection to the conserved quantities at spatial infinity, such as the ADM mass and ADM momentum.